Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions

This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state space in finite time. A barrier certificate condition that b...

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Published in:arXiv.org 2019-05
Main Authors: Santoyo, Cesar, Dutreix, Maxence, Coogan, Samuel
Format: Article
Language:English
Subjects:
Feedback control
Markov analysis
Mathematical analysis
Numerical analysis
Optimization
Polynomials
Probability theory
Safety
State feedback
Stochastic systems
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Dutreix, Maxence
Coogan, Samuel
description This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state space in finite time. A barrier certificate condition that bounds the infinitesimal generator of the system, and hence bounds the expected value of the barrier function over the time horizon, is recast as a sum-of-squares optimization problem for efficient numerical computation. Unlike prior works, the proposed certificate condition includes a state-dependent bound on the infinitesimal generator, allowing for tighter probability bounds. Moreover, for stochastic systems for which the drift dynamics are affine-in-control, we propose a method for synthesizing polynomial state feedback controllers that achieve a specified probability of safety. Two case studies are presented that benchmark and illustrate the performance of our method.
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subjects Feedback control
Markov analysis
Mathematical analysis
Numerical analysis
Optimization
Polynomials
Probability theory
Safety
State feedback
Stochastic systems
title Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions
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